Spaniard Garcia, who had not won a title since the 2002 Korean Open, holed a 15-foot birdie putt at the first extra hole after both players had finished level on 14-under 274 at the par-72 Gary Player Country Club.
The 23-year-old Garcia, who claimed the $1,2 million first prize, had closed with a 70 while 2001 U.S. Open champion Goosen carded a final-round 69.
Fiji's Vijay Singh returned a 69 to finish third at 11-under 277 with Northern Ireland's Darren Clarke, who shot a best-of-the-day 67, a further shot back in fourth.
It was the second time Garcia had won the tournament at the par-three 16th, having chipped in for a birdie from the fringe of the green to beat South African Ernie Els in a playoff for the 2001 title.
"Retief turned to me after I sank the putt and said: 'You like this hole, don't you?'" Garcia said.
Sunday's victory confirmed that the Spanish Ryder Cup player has finally turned the corner after a year of patiently remodelling his swing under the watchful eye of his coach and father Victor.
"I really feel like my swing is good and getting better and better and I hit some beautiful shots out there," Garcia said.
"I've been fighting hard all year long and I really wanted it today, but sometimes you try to hard. I had to relax."
Last week, the Spaniard threw away a two-shot lead at the Dunlop Phoenix tournament in Japan, carding a final-round 78 to slip back into fourth.
WINNING FEELING
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Garcia started the day one stroke ahead of the field at 12 under par, but bogeyed the first after shanking his nine-iron approach 40 yards right of the green.
"I swung quickly at the ball because I was excited and nervous, but I just had to put it behind me," said the Spaniard.
"I calmed down and said to myself that anything I hit today cannot be worse than that shot."
South African Goosen, who began the final round a shot behind Garcia, birdied the par-five second after hitting a three-wood to 12 feet. He missed the eagle putt but had a tap-in for birdie.
However Garcia finally found his range on the par-four third, sinking a 20-foot birdie putt, and followed that by picking up another shot at the par-three fourth, where his tee shot finished six feet from the hole.
Goosen pulled ahead with a birdie on the par-four sixth, where he nearly holed his approach, but Garcia hit back with a birdie of his own at the difficult par-four eighth.
The smooth-swinging Goosen again took the outright lead on the par-five ninth, needing only a five-iron approach into the island green for a two-putt birdie.
Both players birdied the 10th before Garcia closed with a run of eight consecutive pars. Goosen, however, bogeyed the par-five 14th to drop back into a tie for the lead at 14 under.
The South African had a chance to clinch victory at the last, but missed a 10-foot putt for birdie to take the tournament into extra time.
